sampling theory, how to recover amplitude?

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shanmei

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Any time domain signal is composed of some sinusoidal signals. Each sinusoidal signal with frequency Fin can be recovered by the sampling frequency at least twice of Fin. I know that for the sinusoidal signals, two sampling points can alreay confirm this sinusoidal signal, but how it can recoverd the amplitude??

For example, if the sample points are at A and B, the signal time domain information can be confirmed, but how do we know its sinusoidal amplitude? Thanks.
 

Obviously, as your diagram shows, you need to sample faster than 2f. Applying that sampled signal to a sinc filter will reconstruct the signal.
 
Consider that the Nyquist criterion requires Fin < fs/2 rather than Fin <= fs/2. Your example shows that for very small differences to fs/2, it takes nearly infinite time to recover the amplitude.
 
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